Why is the notion of incorruptibility advanced by some Catholics and some Orthodox when determining the corruptibility or incorruptibility of a saint's relics has never been a part of the beatification or canonization process?
The short answer is no.
Not every saint is expected to have an incorruptible corpse. Although incorruptibility is recognized as supernatural, it is no longer counted as a miracle in the recognition of a saint (The Incorruptibles).
Embalmed bodies were not recognized as incorruptibles. For example, although the body of Pope John XXIII remained in a remarkably intact state after its exhumation, Church officials remarked that the body had been embalmed (Christianity Today) and additionally there was a lack of oxygen in his sealed triple coffin.
Incorruptibility is seen as distinct from the good preservation of a body, or from mummification. Incorruptible bodies are often said to have the odour of sanctity, exuding a sweet or floral, pleasant aroma.
Incorruptibility is not reserved to the Catholic Church alone. There are a number of Orthodox Saints who have incorrupt bodies.
Nowadays the Catholic Church is striving to better understand why some Saints are preserved from corruption, thus seeing if the preservation is indeed miraculous or not. "These saints are in a class by themselves. Even though incorruptibility does not automatically confer sainthood upon the subject, it is still properly appreciated by the Church as a supernatural occurrences. The Church thus seeks the help of scientists and other professional to understand this question in a more modern light!
The lack of formal explanations on this subject seems to stem from the fact that this is an area of expertise for the scientific (professional) community and not the Church to investigate.
"Over the last 15 years, however, a new view of the Incorruptibles has begun to emerge. At the Vatican's request, Italian pathologists, chemists, and radiologists have been poring over the bodies of the ancient men and women interred in church reliquaries. Charged with gleaning new information about the lives of the saints and assisting in the conservation of sacred remains, they have also brought science to the altars of Europe's cathedrals. Already, they have examined more than two dozen saints and beati, shedding light on the mystery of their preservation. While some saints were clearly mummified by their devout followers, others were protected from decay by environmental conditions, raising new questions about incorruptibility. "What is a miracle?" asks Ezio Fulcheri, a pathologist at the University of Genoa and one of the leading researchers on the Incorruptibles. "It's something unexplainable, a special event that may occur in different ways." The causes may seem mysterious "but don't exclude [rare] natural processes that are different from the normal course of things." - The Incorruptible.
Nota Bene: This is my answer to this question.
Within the Orthodox Church, there is no formal, centralized process for determining whether or not an individual should be included in the list of the saints. A good description of what is "required" is on the Orthodox Church in America website:
While the glorification of a saint may be initiated because of miracles, it is not an absolute necessity for canonization. The Roman Catholic Church requires three verified miracles in order to recognize someone as a saint; the Orthodox Church does not require this. There are some saints, including Saint Nicodemos of the Holy Mountain (July 14) and Saint Innocent of Moscow (commemorated March 31), who have not performed any miracles, as far as we know. What is required is a virtuous life of obvious holiness. And a saint’s writings and preaching must be “fully Orthodox,” in agreement with the pure faith that we have received from Christ and the Apostles and taught by the Fathers and the Ecumenical Councils.
Can the Church “make” a saint? The answer is no. Only God can do that. We glorify those whom God Himself has glorified, seeing in their lives true love for God and their neighbors. The Church merely recognizes that such a person has cooperated with God’s grace to the extent that his or her holiness is beyond doubt.
Incorruptibility of relics, if it occurs, is usually incidental to and not some precursor to beatification in the Orthodox Church. Saints are usually venerated by local faithful long before their relics are discovered to be incorrupt or the case for beatification comes before any episcopal synod.
A good example of the process is what is happening in Dallas now with Archbishop Dmitri Royster. People began venerating him almost as soon as he died, in 2011. His body was discovered to be incorrupt this year, as it was being moved from a cemetery to the Cathedral of St. Seraphim. As one witness stated:
We all know that an incorrupt body alone is not a reason for glorification. Having known Vladika for 11 years and seeing the fruits of his life in the Lord, I am personally convinced that he is a saint. I believe that there are many more people all over the country who share that conviction.